Higher-Dimensional Algebraic Geometry stories the class idea of algebraic kinds. This very lively zone of analysis continues to be constructing, yet an awesome volume of information has amassed during the last two decades. The author's aim is to supply an simply obtainable advent to the topic.

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57 We will construct in sections 3 and 4. L(2k+1;2) as well as (a,b) = 1, have the sme homotopy type as the Kummer surface L(a,b;2), S?. We will also construct handlebody decompositions of these surfaces in sections 3 and 4. 25 and the language of framed links (§0), we are ready to give a handlebody decomposition of the half Kummer surface be easy to see the Kummer surface characteristic Let and the other elliptic surfaces of Euler 12T. ~. 1. 1 N n = IT (D.. 2. The attaching spheres of each 1-handle are opposite each other, and the framing of the 2 1 2-handle is zero.

If V - V V oo where V oo is a V . V y 2 = x L 3 - t 11 . In this bounds a 4-ball. to an elliptic surface (except for the singular V - V consists of a cusp fiber over °°, and a section, - 2 . If we perturb the equation, the compactifi- cation can be done equivariantly, and surface. L with one cusp point and with self intersection is a homology sphere, and it is unknown that V 5 - t . which meets the first one transversely and which in now with self intersection 3 V, then the "added part" is defined by the equation: Here we can compoactify = x °° which is a fiver of type II (a cusp fiber) -1 V 2 is the plumbing manifold graph (see §0, appendix), and is compactified to an elliptic surface consists of the fiber over 0 V y (2,3,11) V = V^ fl V, homology sphere L is an elliptic K3 lies in an elliptic K3 f surface as the boundary of a neighborhood of a cusp fiber together with a section.